Leveraging Knowledge

An interview with David Ferguson, SUNY at Stony Brook

One of NSF's current goals (and a goal that is probably shared by
Stony Brook's program in Technology and Society) is to integrate the learning
of science and mathematics with technical education through joint efforts
by science, mathematics and technical faculty. What do you see as the
main challenges in implementing interdisciplinary projects of this type?
What would be the benefits?

The primary benefits of interdisciplinary projects are threefold:

They provide the opportunity for students to use a variety of
conceptual tools and skills to address problems in a context more akin to
what a professional might do on the job, thereby enriching students'
appreciation of and facility with a systems approach.

They allow students to see multiple views of concepts (e.g. rate of
change, modeling) across several disciplines. This allows students to
develop a very different understanding of key mathematics and science
ideas than might be the case with more traditional approaches.

They are often very engaging, thus allowing students of varied
backgrounds, achievement levels, and interests to find a "place." Much of
mathematics and science instruction is hierarchical, allowing little
opportunity for those who cannot or choose not to follow that path to
develop their abilities. Interdisciplinary projects help overcome these
constraints.

I do not mean to imply that there cannot be rich exploratory environments
for learning mathematics and science that do not take an interdisciplinary
approach. However, it would appear to me that the interdisciplinary
perspective should eventually come at some point, whether it be in the
next course or the next year.

The primary challenge to implementing interdisciplinary projects is to get
our educational institutions at every level--pre-college to graduate
school--to look over the high walls of individual disciplinary
boundaries to see common intellectual strands and goals. Perhaps an
equally difficult challenge is to make the institutional changes
(rethinking of departments, reward systems, etc.) that will foster such
work. Currently, one gets the sense that interdisciplinary projects
work, when they do, more in spite of the educational system than
because of it.

Finally, another challenge is to develop assessment approaches that
capture the relevant aspects of learning while remaining practical to
implement.

What other strategies besides interdisciplinary courses might offer
students the opportunity to learn to use mathematics in a variety of
real-world contexts?

Quantitative reasoning and problem solving should have a natural role in
many courses in such areas as the biological and social sciences.
There are many ways of knowing. Quantitative methods, art, music,
poetry, and other human endeavors have different purposes; each
represents a different way of knowing the world. Each way of knowing has
its own assumptions, models, and limitations. Students need to see the
natural interplay of these ways of knowing. This means that even
discipline-specific courses should reflect some of the spirit and
methods of the web of knowledge.

Many mathematicians and mathematics educators worry that in most
interdisciplinary programs mathematics exists to serve science and that
the mathematics itself gets lost. How important is it that students see
mathematics as a separate subject rather than just as a powerful tool in
the service of other subjects?

My own feeling is that we should offer multiple opportunities for students
to learn mathematics. Inquiry approaches that lean largely toward pure
mathematics can be valid and appropriate for many students throughout much
of their education. Similarly, interdisciplinary approaches can be valid
and appropriate for most students. Different curricula may reflect
different mixes of pure, applied and interdisciplinary perspectives. We
should be discussing issues of "emphasis" and timing, rather than giving
"either/or" arguments.

Let me add here that in an interdisciplinary program that spans several
years of a student's education, it is critical that key mathematics ideas
get expanded and developed. I would bet that if an interdisciplinary
program meets that need, some students will develop an interest in the
power of pure mathematical ideas. Indeed, more students may develop an
interest in pure mathematics via an interdisciplinary program than through
a diet of "pure mathematics" projects!

Many mathematics faculty also worry that the context-rich environment of
an interdisciplinary course will impede rather than enhance learning,
since it will be harder for students to sort out the mathematics
principles from the surrounding context. And they worry that students will
not have the opportunity to take the mathematics they are learning to "the
next level." What has been your experience in this regard?

My response benefited from discussions with Michael Hacker, Executive
Director of the NSF-supported Mathematics, Science, and Technology (MST)
project (based at Stony Brook) for fostering elementary school teachers'
abilities to integrate mathematics, science, and technology. (Michael was
formerly with the New York State Education Department.)

An interdisciplinary (e.g., MST) approach need not dilute mathematics,
science, and technology content. In each of the subjects it is important
to identify key ideas or strands and to monitor the progression of these
strands as students move from kindergarten through 12th grade (or into
undergraduate education). That is, we must consider what it means for
students to mature intellectually in these areas. Part of that maturity
should reflect a greater ability to scaffold knowledge and engage in
exploration that will lead to "the next level" of understanding of
concepts, methods, and tools.

The challenge of Interdisciplinary education is to build a progression of
contextual activities that would enable children to construct personally
meaningful knowledge, while at the same time extending their knowledge of
key ideas and concepts.

An interdisciplinary and process-oriented approach to the learning and
teaching of mathematics, science, and technology need not compromise
content or cohesiveness of central ideas in any of these subject areas.
By emphasizing process and applications, students gain additional tools
that enable them to leverage their knowledge and thereby learn more, not
less content. Also, when knowledge is personally meaningful, it offers
opportunities for the learner to dig deeper into concepts. We should not
be misled into thinking that the barrage of techniques that exemplify much
of mathematics education and the horde of "recipes" so common in science
"labs" means "more content."

Let's give students the opportunity to dig more deeply and the tools to
explore new domains. That should be the real meaning of "more content."

David Ferguson is an applied mathematician and mathematics educator at
the State University of New York at Stony Brook where he directs the
Educational Computing Program in the Program in Technology and Society.
He can be reached via email atdferguson@dts.tns.sunysb.edu.